Effect of thrombin inhibitors on positive feedback in the coagulation cascade

The coagulation cascade is a series of sequential reactions of limited proteolysis of protein factors resulting in generation of thrombin. Thrombin mediates both positive and negative feedback in regulating this cascade by taking part in activation of several factors. Some thrombin inhibitors, by affecting positive feedback, inhibit generation of thrombin itself. In the current study, we used two thrombin inhibitors: argatroban, a low molecular weight reversible competitive inhibitor that binds to the active site, and bivalirudin, a bivalent oligopeptide that blocks the active site and binding center of protein substrates (exosite I). Appearance rate and total amount of thrombin were measured in a thrombin generation assay (TGA) using a fluorescent substrate. We found that argatroban slows the appearance of thrombin and lowers its amount. Bivalirudin also slows appearance of thrombin, but it does not decrease its amount, perhaps because the region being bound to the active site undergoes hydrolysis so that the inhibitor stops binding to thrombin. Many reactions of the coagulation cascade proceed on the surface of phospholipid micelles (PLMs). In the case of argatroban, PLMs do not affect the results of the TGA, whereas for bivalirudin they lower its inhibitory activity. It seems that PLMs stabilize protein complexes (wherein thrombin exosite I is hindered) mediating positive feedback in the coagulation cascade, e.g. complexes of thrombin with factor V and VIII.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Distinguishing reversible from irreversible virus capsid assembly

Capsids of spherical viruses may be constructed from hundreds or thousands of copies of the major capsid protein(s). These assembly reactions are poorly understood. Here we consider the predicted behavior for assembly where the component reactions have weak association energy and are reversible and compare them to essentially irreversible reactions. The comparisons are based on mass action calculations and the behavior predicted from kinetic simulations where assembly is described as a cascade of low order reactions. Reversible reactions are characterized by a pseudo-critical concentration, whereas irreversible reactions consume all free subunits. Irreversible reactions are more susceptible to kinetic traps comprised of numerous small intermediates. In the case where only the ultimate step is irreversible, very low concentrations of intermediates slow the completion of the reaction so that overall it closely matches the predictions for the reversible reactions that make up the majority of the cascade. Data in the literature strongly support the hypothesis that most viruses are held together by many weak interactions.     

Systems Biology of Coagulation Initiation: Kinetics of Thrombin Generation in Resting and Activated Human Blood

Blood function defines bleeding and clotting risks and dictates approaches for clinical intervention. Independent of adding exogenous tissue factor (TF), human blood treated in vitro with corn trypsin inhibitor (CTI, to block Factor XIIa) will generate thrombin after an initiation time (T_i) of 1 to 2 hours (depending on donor), while activation of platelets with the GPVI-activator convulxin reduces T_i to ∼20 minutes. Since current kinetic models fail to generate thrombin in the absence of added TF, we implemented a Platelet-Plasma ODE model accounting for: the Hockin-Mann protease reaction network, thrombin-dependent display of platelet phosphatidylserine, VIIa function on activated platelets, XIIa and XIa generation and function, competitive thrombin substrates (fluorogenic detector and fibrinogen), and thrombin consumption during fibrin polymerization. The kinetic model consisting of 76 ordinary differential equations (76 species, 57 reactions, 105 kinetic parameters) predicted the clotting of resting and convulxin-activated human blood as well as predicted T_i of human blood under 50 different initial conditions that titrated increasing levels of TF, Xa, Va, XIa, IXa, and VIIa. Experiments with combined anti-XI and anti-XII antibodies prevented thrombin production, demonstrating that a leak of XIIa past saturating amounts of CTI (and not “blood-borne TF” alone) was responsible for in vitro initiation without added TF. Clotting was not blocked by antibodies used individually against TF, VII/VIIa, P-selectin, GPIb, protein disulfide isomerase, cathepsin G, nor blocked by the ribosome inhibitor puromycin, the Clk1 kinase inhibitor Tg003, or inhibited VIIa (VIIai). This is the first model to predict the observed behavior of CTI-treated human blood, either resting or stimulated with platelet activators. CTI-treated human blood will clot in vitro due to the combined activity of XIIa and XIa, a process enhanced by platelet activators and which proceeds in the absence of any evidence for kinetically significant blood borne tissue factor.     

Glutathione Synthesis and Turnover in the Human Erythrocyte: ALIGNMENT OF A MODEL BASED ON DETAILED ENZYME KINETICS WITH EXPERIMENTAL DATA

The erythrocyte is exposed to reactive oxygen species in the circulation and also to those produced by autoxidation of hemoglobin. Consequently, erythrocytes depend on protection by the antioxidant glutathione. Mathematical models based on realistic kinetic data have provided valuable insights into the regulation of biochemical pathways within the erythrocyte but none have satisfactorily accounted for glutathione metabolism. In the current model, rate equations were derived for the enzyme-catalyzed reactions, and for each equation the nonlinear algebraic relationship between the steady-state kinetic parameters and the unitary rate constants was derived. The model also includes the transport processes that supply the amino acid constituents of glutathione and the export of oxidized glutathione. Values of the kinetic parameters for the individual reactions were measured predominately using isolated enzymes under conditions that differed from the intracellular environment. By comparing the experimental and simulated results, the values of the enzyme-kinetic parameters of the model were refined to yield conformity between model simulations and experimental data. Model output accurately represented the steady-state concentrations of metabolites in erythrocytes suspended in plasma and the changing glutathione concentrations in whole and hemolyzed erythrocytes under specific experimental conditions. Analysis indicated that feedback inhibition of γ-glutamate-cysteine ligase by glutathione had a limited effect on steady-state glutathione concentrations and was not sufficiently potent to return glutathione concentrations to normal levels in erythrocytes exposed to sustained increases in oxidative load.     

Multi-step rhodopsin inactivation schemes can account for the size variability of single photon responses in Limulus ventral photoreceptors

Limulus ventral photoreceptors generate highly variable responses to the absorption of single photons. We have obtained data on the size distribution of these responses, derived the distribution predicted from simple transduction cascade models and compared the theory and data. In the simplest of models, the active state of the visual pigment (defined by its ability to activate G protein) is turned off in a single reaction. The output of such a cascade is predicted to be highly variable, largely because of stochastic variation in the number of G proteins activated. The exact distribution predicted is exponential, but we find that an exponential does not adequately account for the data. The data agree much better with the predictions of a cascade model in which the active state of the visual pigment is turned off by a multi-step process.     

Computationally derived points of fragility of a human cascade are consistent with current therapeutic strategies

The role that mechanistic mathematical modeling and systems biology will play in molecular medicine and clinical development remains uncertain. In this study, mathematical modeling and sensitivity analysis were used to explore the working hypothesis that mechanistic models of human cascades, despite model uncertainty, can be computationally screened for points of fragility, and that these sensitive mechanisms could serve as therapeutic targets. We tested our working hypothesis by screening a model of the well-studied coagulation cascade, developed and validated from literature. The predicted sensitive mechanisms were then compared with the treatment literature. The model, composed of 92 proteins and 148 protein-protein interactions, was validated using 21 published datasets generated from two different quiescent in vitro coagulation models. Simulated platelet activation and thrombin generation profiles in the presence and absence of natural anticoagulants were consistent with measured values, with a mean correlation of 0.87 across all trials. Overall state sensitivity coefficients, which measure the robustness or fragility of a given mechanism, were calculated using a Monte Carlo strategy. In the absence of anticoagulants, fluid and surface phase factor X/activated factor X (fX/FXa) activity and thrombin-mediated platelet activation were found to be fragile, while fIX/FIXa and fVIII/FVIIIa activation and activity were robust. Both anti-fX/FXa and direct thrombin inhibitors are important classes of anticoagulants; for example, anti-fX/FXa inhibitors have FDA approval for the prevention of venous thromboembolism following surgical intervention and as an initial treatment for deep venous thrombosis and pulmonary embolism. Both in vitro and in vivo experimental evidence is reviewed supporting the prediction that fIX/FIXa activity is robust. When taken together, these results support our working hypothesis that computationally derived points of fragility of human relevant cascades could be used as a rational basis for target selection despite model uncertainty.     

Affinity analysis of non-steady-state data obtained under mass transport limited conditions using BIAcore technology

Binding data obtained with Biacore instrumentation is often evaluated using a kinetic transport model where reaction rate constants and a mass transport coefficient are used to describe the interaction. Here the use of a simplified model, an affinity transport model, for determination of the affinity (K(D)) but not the kinetics (k(a), k(d)) has been investigated. When binding rates were highly governed by mass transport effects the two models returned the same affinity and gave similar residuals, but k(a) and k(d) values found with the kinetic transport model were unreliable. On the other hand the affinity transport model failed to describe the data when binding curves were less influenced by mass transport effects. Under such circumstances the kinetic transport model returned correct k(a) and k(d) values. Depending on the outcome of the analysis the affinity transport model can therefore be used to reduce uncertainties of the kinetic parameters or as an easy way to determine K(D) values from non-steady-state data. The use of the affinity transport model is illustrated with simulated data and with binding data obtained for the interaction between a 439 Da thrombin inhibitor and immobilized thrombin. Since it is more difficult to resolve high k(a) values for low molecular weight analytes, the affinity transport model may be particularly useful for affinity analysis involving fast reactions between such analytes and immobilized protein targets.     

The use of automated parameter searches to improve ion channel kinetics for neural modeling

The voltage and time dependence of ion channels can be regulated, notably by phosphorylation, interaction with phospholipids, and binding to auxiliary subunits. Many parameter variation studies have set conductance densities free while leaving kinetic channel properties fixed as the experimental constraints on the latter are usually better than on the former. Because individual cells can tightly regulate their ion channel properties, we suggest that kinetic parameters may be profitably set free during model optimization in order to both improve matches to data and refine kinetic parameters. To this end, we analyzed the parameter optimization of reduced models of three electrophysiologically characterized and morphologically reconstructed globus pallidus neurons. We performed two automated searches with different types of free parameters. First, conductance density parameters were set free. Even the best resulting models exhibited unavoidable problems which were due to limitations in our channel kinetics. We next set channel kinetics free for the optimized density matches and obtained significantly improved model performance. Some kinetic parameters consistently shifted to similar new values in multiple runs across three models, suggesting the possibility for tailored improvements to channel models. These results suggest that optimized channel kinetics can improve model matches to experimental voltage traces, particularly for channels characterized under different experimental conditions than recorded data to be matched by a model. The resulting shifts in channel kinetics from the original template provide valuable guidance for future experimental efforts to determine the detailed kinetics of channel isoforms and possible modulated states in particular types of neurons.     

Dynamics and mechanisms of coupled protein folding and binding reactions

Protein folding coupled to binding of a specific ligand is frequently observed in biological processes. In recent years numerous studies have addressed the structural properties of the unfolded proteins in the absence of their ligands. Surprisingly few time-resolved investigations on coupled folding and binding reactions have been published up to date and the dynamics and kinetic mechanisms of these processes are still only poorly understood. Especially, it is still unsolved for most systems which conformation of the protein is recognized by the ligand (conformational selection vs. folding-after-binding) and whether the ligand influences the folding kinetics. Here we review experimental methods, kinetic models and time-resolved experimental studies of coupled folding and binding reactions.     

A model for the stoichiometric regulation of blood coagulation

We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF).VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by "exposing" picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described.     

Kitasatospora sp. MY5-36产ε-聚赖氨酸分批补料发酵动力学

以北里孢菌(Kitasatospora sp.)MY 5-36为供试菌株,对ε-聚赖氨酸分批补料发酵动力学模型进行研究。建立了该菌株发酵合成ε-聚赖氨酸的菌体生长、产物合成和总糖消耗的动力学模型,并通过Origin 8.1软件对模型参数进行非线性拟合。结果表明:菌体量和聚赖氨酸的产量分别为16.25和13.15 g/L,产物合成与菌体生长的关系为部分耦联型。经验证,预测值与实验值有良好的拟合性,拟合度分别为0.999、0.995和0.992,说明所构建模型能够较好地反映ε-聚赖氨酸分批补料发酵过程。     

Protease nexin 1 is a potent urinary plasminogen activator inhibitor in the presence of collagen type IV

Protease nexin 1 (PN1) in solution forms inhibitory complexes with thrombin or urokinase, which have opposing effects on the blood coagulation cascade. An initial report provided data supporting the idea that PN1 target protease specificity is under the influence of collagen type IV (1). Although collagen type IV demonstrated no effect on the association rate between PN1 and thrombin, the study reported that the association rate between PN1 and urokinase was allosterically reduced 10-fold. This has led to the generally accepted idea that the primary role of PN1 in the brain is to act as a rapid thrombin inhibition and clearance mechanism during trauma and loss of vascular integrity. In studies to identify the structural determinants of PN1 that mediate the allosteric interaction with collagen type IV, we found that protease specificity was only affected after transient exposure of PN1 to acidic conditions that mimic the elution protocol from a monoclonal antibody column. Because PN1 used in previous studies was purified over a monoclonal antibody column, we propose that the allosteric regulation of PN1 target protease specificity by collagen type IV is a result of the purification protocol. We provide both biochemical and kinetic data to support this conclusion. This finding is significant because it implies that PN1 may play a much larger role in the modeling and remodeling of brain tissues during development and is not simply an extravasated thrombin clearance mechanism as previously suggested.     

Intra‐specific variability and plasticity influence potential tree species distributions under climate change

Aim To assess the effect of local adaptation and phenotypic plasticity on the potential distribution of species under future climate changes. Trees may be adapted to specific climatic conditions; however, species range predictions have classically been assessed by species distribution models (SDMs) that do not account for intra‐specific genetic variability and phenotypic plasticity, because SDMs rely on the assumption that species respond homogeneously to climate change across their range, i.e. a species is equally adapted throughout its range, and all species are equally plastic. These assumptions could cause SDMs to exaggerate or underestimate species at risk under future climate change. Location The Iberian Peninsula. Methods Species distributions are predicted by integrating experimental data and modelling techniques. We incorporate plasticity and local adaptation into a SDM by calibrating models of tree survivorship with adaptive traits in provenance trials. Phenotypic plasticity was incorporated by calibrating our model with a climatic index that provides a measure of the differences between sites and provenances. Results We present a new modelling approach that is easy to implement and makes use of existing tree provenance trials to predict species distribution models under global warming. Our results indicate that the incorporation of intra‐population genetic diversity and phenotypic plasticity in SDMs significantly altered their outcome. In comparing species range predictions, the decrease in area occupancy under global warming conditions is smaller when considering our survival–adaptation model than that predicted by a ‘classical SDM’ calibrated with presence–absence data. These differences in survivorship are due to both local adaptation and plasticity. Differences due to the use of experimental data in the model calibration are also expressed in our results: we incorporate a null model that uses survival data from all provenances together. This model always predicts less reduction in area occupancy for both species than the SDM calibrated with presence–absence. Main conclusions We reaffirm the importance of considering adaptive traits when predicting species distributions and avoiding the use of occurrence data as a predictive variable. In light of these recommendations, we advise that existing predictions of future species distributions and their component populations must be reconsidered.     

Inhibition of platelet-surface-bound proteins during coagulation under flow II: Antithrombin and heparin

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Antithrombin (AT) is one such inhibitor that impedes coagulation by targeting and inactivating several key coagulation enzymes. The effect of AT is greatly enhanced in the presence of heparin, a common anticoagulant drug. When heparin binds to AT, it either bridges with the target enzyme or induces allosteric changes in AT leading to more favorable binding with the target enzyme. AT inhibition of fluid-phase enzymes caused little suppression of thrombin generation in our previous mathematical models of blood coagulation under flow. This is because in that model, flow itself was a greater inhibitor of the fluid-phase enzymes than AT. From clinical observations, it is clear that AT and heparin should have strong inhibitory effects on thrombin generation, and thus we hypothesized that AT could be inhibiting enzymes bound to activated platelet surfaces that are not subject to being washed away by flow. We extended our mathematical model to include the relevant reactions of AT inhibition at the activated platelet surfaces as well as those for unfractionated heparin and a low molecular weight heparin. Our results show that AT alone is only an effective inhibitor at low tissue factor densities, but in the presence of heparin, it can greatly alter, and in some cases shut down, thrombin generation. Additionally, we studied each target enzyme separately and found that inactivation of no single enzyme could substantially suppress thrombin generation.     

Prediction of Rate‐Limiting Reactions for Growth‐Associated Production Using a Constraint‐Based Approach

Identification of a rate‐limiting step in pathways is a key challenge in metabolic engineering. Although the prediction of rate‐limiting steps using a kinetic model is a powerful approach, there are several technical hurdles for developing a kinetic model. In this study, an in silico screening algorithm of key enzyme for metabolic engineering is developed to identify the possible rate‐limiting reactions for the growth‐coupled target production using a stoichiometric model without any experimental data and kinetic parameters. In this method, for each reaction, an upper‐bound flux constraint is imposed and the target production is predicted by linear programming. When the constraint decreases the target production at the optimal growth state, the reaction is thought to be a possible rate‐limiting step. For validation, this method is applied to the production of succinate or 1,4‐butanediol (1,4‐BDO) in Escherichia coli, in which the experimental engineering for eliminating rate‐limiting steps has been previously reported. In succinate production from glycerol, nine reactions including phosphoenolpyruvate carboxylase are predicted as the rate‐limiting steps. In 1,4‐BDO production from glucose, eight reactions including pyruvate dehydrogenase are predicted as the rate‐limiting steps. These predictions include experimentally identified rate‐limiting steps, which would contribute to metabolic engineering as a practical tool for screening candidates of rate‐limiting reactions.